Find the $$ n t h $$ term of the sequ $$ \text { (i) } 24,12,6,3, \ldots $$

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UpStudy AI · Accepted Answer

**Step 1: Identify the Pattern**

The sequence is $$ 24, 12, 6, 3, \ldots $$. Notice that each term is obtained by dividing the previous term by $$ 2 $$. This indicates that the sequence is geometric with a common ratio $$ r = \frac{1}{2} $$.

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**Step 2: Write the General Formula for a Geometric Sequence**

For a geometric sequence, the $$ n^{th} $$ term is given by:
$$
a_n = a \cdot r^{n-1}
$$
where $$ a $$ is the first term and $$ r $$ is the common ratio.

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**Step 3: Substitute Values**

Here, $$ a = 24 $$ and $$ r = \frac{1}{2} $$. Substituting these values into the formula:
$$
a_n = 24 \cdot \left(\frac{1}{2}\right)^{n-1}
$$

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**Step 4: Final Answer**

The $$ n^{th} $$ term of the sequence is:
$$
a_n = 24 \cdot \left(\frac{1}{2}\right)^{n-1}
$$
The $$ n^{th} $$ term of the sequence is $$ a_n = 24 \cdot \left(\frac{1}{2}\right)^{n-1} $$.

Find the \( n t h \) term of the sequ \[ \text { (i) } 24,12,6,3, \ldots \]

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